{"schema":"vela.problem-packet.v0.1","problem":604,"statement":"Given $n$ distinct points $A\\subset\\mathbb{R}^2$ must there be a point $x\\in A$ such that\\[\\#\\{ d(x,y) : y \\in A\\} \\gg n^{1-o(1)}?\\]Or even $\\gg n/\\sqrt{\\log n}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}